If angle $A$ lies in the second quadrant and $\sin A = \frac{3}{4},$ find $\cos A.$
Answer: Since angle $A$ lies in the second quadrant, $\cos A$ is negative.  Also,
\[\cos^2 A = 1 - \sin^2 A = 1 - \frac{9}{16} = \frac{7}{16},\]so $\cos A = \boxed{-\frac{\sqrt{7}}{4}}.$